The present invention is directed to a method and apparatus for separating a signal mix ##EQU1## that is composed of M known, real or complex functions f.sub..mu. (t) that are weighted with the unknown weighting factors g.sub..mu., .mu.=1, 2 . . . M, whereby all or some of the functions f.sub..mu. (t) are chronologically and/or spectrally not disjunctive, and whereby an additional noise signal n(t) can be superimposed on the signal mix s(t).
It is assumed in the present specification that the functions f.sub..mu. (t) are real. The transition to complex functions f.sub..mu. (t) is possible without further ado. See reference #3.
It is known that the problem of signal separation is in acquiring estimated values g.sub..mu. for the unknown weighting factors g.sub..mu. from the signal mix s(t) according to equation (1). According to the prior art (see reference #1), the estimating of the weighting factors g.sub..mu. proceeds according to a method that correlates the signal mix s(t) according to equation (1) with each of the known functions f.sub..mu. (t) and to consider the M correlation products f.sub..mu. thereby acquired as estimated values g.sub..mu. for the unknown weighting factors g.sub..mu.. FIG. 1 shows an apparatus with which this method of the prior art is implemented. This arrangement is composed of M filters (1) having the pulse responses h.sub..mu. (t), .mu.=1, 2, . . . M and of M samplers (2), whereby each of the M filters (1) is signal-matched to respectively exactly one of the functions f.sub..mu. (t) and is thus independent in terms of its properties from the respective M-1 remaining functions f.sub..mu. (t). When white, Gaussian noise is assumed as noise signal n(t), signal matching means that the relationship EQU h.sub..mu. (t)=A.multidot.f.sub..mu. (T-t) (2)
exists between the function f.sub..mu. (t) and the pulse response of the corresponding, .mu..sup.th signal-matched filter (see reference #2). For other types of noise signal, the pulse response h.sub..mu. (t) is to be correspondingly modified (see reference #2). The amplitude factor A and the delay time T in equation (2) can be equated with one or, respectively, zero without limiting the universality in the following considerations. Instead of signal-matched filters (1), correlators can also be utilized in the arrangement of FIG. 1 because of the known equivalency of correlation and signal-matched filtering (see reference #2).
When the signal mix s(t) according to equation (1) is supplied to the arrangement of FIG. 1, then samples w.sub..mu., .mu.=1, 2 . . . M that correspond to the correlation products of the signal mix s(t) according to equation (1) and respectively one of the M functions f.sub..mu. (t), .mu.=1, 2 . . . M are obtained by chronologically correct sampling of the M filter output signals with the samplers (2). When the pulse response h.sub..mu. (t) of the signal-matched filters is selected according to equation (2) and when A is equated to one and T is equated to zero, then the samples w.sub..mu. in the undisturbed case read ##EQU2## The integration interval T.sub.int in equation (3) is to be selected such that the entire time domain in which the functions f.sub..mu. (t) can assume values not equal to zero is covered.
As known, the samples w.sub..mu. according to equation (3) can be considered estimated values g.sub..mu., .mu.=1, 2 . . . M of the weighting factor g.sub..mu. (see reference #1). As also known, however, these estimated values g.sub..mu. are falsified in that the signal component g.sub..mu. .multidot.f.sub..mu. (t) of the signal mix s(t) according to equation (1) generates a voltage not only at the output of the .mu..sup.th signal-matched filter allocated to it but also at the outputs of the M-1 other signal-matched filters. These falsifications are referred to as bias (see reference #3). It is also reported that the estimate is not true to expectation (see reference #3). Such a bias of the estimated values g.sub..mu. would not appear, given use of the arrangement according to FIG. 1, only in the specific instance that all functions f.sub..mu. (t) are exactly orthogonal relative to one another, this usually not being present in practice.
The appearance of the afore-mentioned bias given use of functions f.sub..mu. (t) that are not exactly orthogonal is a serious disadvantageous of the previously known method for separating a signal mix according to equation (1) and of the corresponding arrangement according to FIG. 1. According to the prior art (see reference #2), attempts are made to counter this disadvantage by using only specifically selected or, respectively, construed functions f.sub..mu. (t) that come as close as possible to the case of orthogonality. This procedure, however, has the obvious disadvantage that the selection of the functions f.sub..mu. (t) is limited. However, freedom in the selection is desirable, for example when the functions f.sub..mu. (t) are to be frequently changed in order to achieve protection against interception in a message transmission system. In many instances, the functions f.sub..mu. (t) are also prescribed, so that the possibility of selecting specific functions f.sub..mu. (t) is not established a priori. The prior art in signal separation is thus unsatisfactory.